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GRANTING that the commonly accepted estimate of the im-
portance of what Copernicus did is correct, we shall have to
admit that it is either the highest praise or the severest con-
demnation humanly possible to call another man the 'Coper-
nicus' of anything. When we understand what Lobatchewsky
did in the creation of non-Euclidean geometry, and consider
its significance for all human thought, of which mathematics is
only a small if important part, we shall probably agree that
Clifford (1845-79), himself a great geometer and far more than
a 'mere mathematician*, was not overpraising his hero when he
called Lobatchewsky 'The Copernicus of Geometry*.
Nikolas Ivanovitch Lobatchewsky, the second son of a minor
government official, was born on 2 November 1793 in the
district of Makarief, government of Nijni Novgorod, Russia.
The father died when Nikolas was seven, leaving his widow,
Praskovia Ivanovna, the care of three young sons. As the
father's salary had barely sufficed to keep his family going
while he was alive the widow found herself in extreme poverty.
She moved to Kazan, where she prepared her boys for school as
best she could, and had the satisfaction of seeing them accepted,
one after the other, as free scholars at the Gymnasium. Nikolas
was admitted in 1802 at the age of eight. His progress was
phenomenally rapid in both mathematics and the classics* At
the age of fourteen he was ready for the university. In 1807 he
entered the University of Kazan (founded hi 1805), where he